The number 1521
1521 is a perfect square (39²). Its prime factorisation is × . Divisors (9): 1, 3, 9, 13, 39, 117, 169, 507, 1521.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1521: a perfect square (39²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
1521 is composite. Its prime factorisation is
- 3
The divisors add up to 2379; without 1521 itself that is 858, so 1521 is deficient (858 is less than 1521). Euler's totient φ(1521) = 936 numbers up to 1521 share no factor with it.
- 4
The digits of 1521 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 109 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1521 = 3^{2} \times 13^{2} \]1521 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 2379 |
| Euler totient φ(n) | 936 |
| Square | 2313441 |
| Cube | 3518743761 |
| Square root | 39 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 109 |
| Scientific notation | 1.521 × |
| Perfect power |
1521 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and twenty-one |
| Roman numerals | MDXXI |
| Binary (base 2) | 10111110001 |
| Octal (base 8) | 2761 |
| Hexadecimal (base 16) | 5F1 |
| Base 3 | 2002100 |
| As time | 1521 seconds = 25 min 21 s |
Is 1521 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1521 ÷ 3 = 507) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1521 ÷ 9 = 169) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1521 a prime number?
No. 1521 = × , so it is divisible by 3.
What are the factors of 1521?
1, 3, 9, 13, 39, 117, 169, 507, 1521.
What is 1521 in binary?
10111110001 (hexadecimal 5F1, octal 2761).
What is the square root of 1521?
39, because 39 × 39 = 1521.
What is 1521 in Roman numerals?
MDXXI.
Is 1521 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1521?
1521 is a perfect square (39²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.